Geometry of chiral temporal structures I: Physical effects

TL;DR

This paper introduces the concept of temporal geometry in non-relativistic physics, exploring how Berry curvature and connection influence ultrafast chiral electron dynamics and enabling control of enantio-sensitive processes.

Contribution

It pioneers the application of geometric and topological concepts to temporal structures in electron dynamics, revealing new control mechanisms using tailored laser fields.

Findings

Berry curvature depends on light polarization

Temporal geometry applies to multiphoton processes

Control of enantio-sensitive observables via laser fields

Abstract

In non-relativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and topological properties of temporal shapes, i.e. trajectories traced by the tip of a time-dependent vector in vector space. We apply it to vectors describing ultrafast electron currents or induced polarization in chiral molecules. The central concepts of temporal geometry - Berry curvature and Berry connection - emerge as ubiquitous features of photoexcited, non-equilibrium, chiral electron dynamics. We demonstrate that the Berry curvature and Berry connection (i) rely on the polarization properties of light pulses, (ii) can be introduced for multiphoton processes, and (iii) control enantio-sensitive geometric observables via non-equilibrium electronic dynamics excited by tailored laser fields. Our findings may open a way to ultrafast, topologically non-trivial, and enantio-sensitive chemical dynamics.